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Abstract

This paper proposes a solution to the spectral color constancy problem. The method is based on a statistical model for the surface reflectance spectrum and applies a maximum entropy constraint. Unlike prior methods based on linear models, the solution process does not require a set of basis functions to be defined, nor does it require a database of spectra to be specified in advance. Experiments on simulated and real data show that spectral estimation using the maximum entropy approach is feasible and performs similarly to existing spectral methods in spite of the lower level of a priori information required.

References

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Table 1

Average and Median of the RMSEs in Surface Patch and Illuminant Spectral Estimates in All Munsell Scenes for Simulation and Experimental Data

Scene Type

Surfaces Average

Surfaces Median

Illuminants Average

Illuminants Median

Simulation (all lights)

0.1704

0.1539

0.1747

0.1650

Simulation (tungsten)

0.1800

0.1048

0.2197

0.2422

Experiment (tungsten)

0.1652

0.1379

0.4577

0.4590

Table 2

Average and Median of the RMSEs in Surface Patch and Illuminant Spectral Estimates in All Scenes for the Maximum Entropy Approach and the Bayesian Approacha

Scene Component

Maximum Entropy Average

Maximum Entropy Median

Bayesian Average

Bayesian Median

Surface Patches

0.2930

0.2498

0.3063

0.2969

Illuminants

0.3376

0.3365

0.2047

0.1678

a Simulations were carried out in the presence of noise.

Table 3

Median of the Euclidean Distances for the Chromaticities of the Illuminant Estimates of 100 Scenes (72 Scenes for 2D Gamut Mapping) Given by Five Main Previous Approaches with Their Corresponding Variations (When Applicable) and Our Maximum Entropy Approacha

Algorithm

Median Euclidean Distance Error

2D Gamut Mapping—MV

0.0607

2D Gamut Mapping—ICA

0.0554

GW

0.0490

Scale-by-Max

0.0478

2D Gamut Mapping—AVE

0.0455

DB-GW

0.0436

C-by-C-MLM

0.0424

3D Gamut Mapping—ICA

0.0423

3D Gamut Mapping—AVE

0.0422

C-by-C-MAP

0.0420

3D Gamut Mapping—MV

0.0409

C-by-C-MMSE

0.0406

C-by-C-01

0.0288

Maximum Entropy approach

0.0310

a Median errors of the previous approaches are listed in decreasing order.

Tables (3)

Table 1

Average and Median of the RMSEs in Surface Patch and Illuminant Spectral Estimates in All Munsell Scenes for Simulation and Experimental Data

Scene Type

Surfaces Average

Surfaces Median

Illuminants Average

Illuminants Median

Simulation (all lights)

0.1704

0.1539

0.1747

0.1650

Simulation (tungsten)

0.1800

0.1048

0.2197

0.2422

Experiment (tungsten)

0.1652

0.1379

0.4577

0.4590

Table 2

Average and Median of the RMSEs in Surface Patch and Illuminant Spectral Estimates in All Scenes for the Maximum Entropy Approach and the Bayesian Approacha

Scene Component

Maximum Entropy Average

Maximum Entropy Median

Bayesian Average

Bayesian Median

Surface Patches

0.2930

0.2498

0.3063

0.2969

Illuminants

0.3376

0.3365

0.2047

0.1678

a Simulations were carried out in the presence of noise.

Table 3

Median of the Euclidean Distances for the Chromaticities of the Illuminant Estimates of 100 Scenes (72 Scenes for 2D Gamut Mapping) Given by Five Main Previous Approaches with Their Corresponding Variations (When Applicable) and Our Maximum Entropy Approacha

Algorithm

Median Euclidean Distance Error

2D Gamut Mapping—MV

0.0607

2D Gamut Mapping—ICA

0.0554

GW

0.0490

Scale-by-Max

0.0478

2D Gamut Mapping—AVE

0.0455

DB-GW

0.0436

C-by-C-MLM

0.0424

3D Gamut Mapping—ICA

0.0423

3D Gamut Mapping—AVE

0.0422

C-by-C-MAP

0.0420

3D Gamut Mapping—MV

0.0409

C-by-C-MMSE

0.0406

C-by-C-01

0.0288

Maximum Entropy approach

0.0310

a Median errors of the previous approaches are listed in decreasing order.